Estimating Activity and Size in a Zero-Inflated Fill Model

Consider a toy fill-size model for a child order. With probability $1-p$, no fill occurs and the observed size is $0$. With probability $p$, a fill occurs and the size is exponentially distributed with rate $\lambda$.

The empirical mean fill size is $2$ and the empirical variance is $12$.

Use the method of moments to estimate $p$ and $\lambda$.